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Rank Test Based On Matrix Perturbation Theory

  • Zaka Ratsimalahelo
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    In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated singular values. Using Matrix Perturbation Theory, the smallest singular values of random matrix converge asymptotically to zero in the order O(N-1) and the corresponding left and right singular vectors converge asymptotically in the order O(N-1/2). Moreover, the asymptotic distribution of the test statistic is seen to be chi-squared. The test has advantages over standard tests in being easier to compute. Two approaches are be considered sequential testing strategy and information theoretic criterion. We establish a strongly consistent of the determination of the rank of matrix using both the two approaches. Some economic applications are discussed and simulation evidence is given for this test. Its performance is compared to that of the LDU rank tests of Gill and Lewbel (1992) and Cragg and Donald (1996).

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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2001_04.pdf
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    Paper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2001_04.

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    Length: 38 pages
    Date of creation: Jul 2001
    Date of revision:
    Handle: RePEc:eei:rpaper:eeri_rp_2001_04
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